# [music-dsp] Whats wrong with my FFT?

John Stewart jstewart at sdl.psych.wright.edu
Fri Apr 20 04:22:37 EDT 2001

```On Thu, 19 Apr 2001, robert bristow-johnson wrote:

> i looked at http://www.student.oulu.fi/~oniemita/DSP/golay.txt and i
> couldn't figger out this Golay stuff either.  do you mind explaining it,
> John?

I'm not a much of a mathematician or theoritician but I can
brain dump what I know and see if you can figure it out from there.
The nifty thing with golay codes is that the autocorrelation of the
a and b sequences have side lobes that cancel each other out when
they're summed leaving just an impulse.  Take for example the length
2^2 golay codes:
a=[1 1  1 -1]
b=[1 1 -1  1]

xcorr(a,a)=[-1 0  1 4  1 0 -1]
xcorr(b,b)=[ 1 0 -1 4 -1 0  1]
sum  [ 0 0  0 8  0 0  0]  an impulse

Thus by mystical handwaving you can compute the impulse response
given a pair of golay responses and the original golay codes like so:
ir=xcorr(a,ar)+xcorr(b,br);

That's about all I can think of right now.

I did a few google searches on "golay codes" and "golay
complementary sequences" I didn't find much that seemed directly
applicable to using them for collecting impulse responses, though
I did see a reference that I recall being mentioned when I was
introduced to golay codes:

S. Foster. Impulse response measurements using golay codes. IEEE
Conference on Acoustics, Speech and Signal Processing, 2:929932, 1986.

John Stewart

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